Codebook generating method and apparatus for generating a codebook for multi-polarized multiple-input multiple-output (mimo) systems

ABSTRACT

A communication apparatus and method include: selecting, as a precoding matrix, one of pre-stored at least one matrix W i , where i is a natural number, and precoding a data stream desired to be transmitted based on the precoding matrix, wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W i , includes a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, includes the zero matrix

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 12/025,910, filed on Feb. 5, 2008, which claims the benefit of U.S. Provisional Application No. 60/899,634, filed on Feb. 6, 2007, and U.S. Provisional Application No. 60/929,032, filed on Jun. 8, 2007, both filed in the U.S. Patent and Trademark office; and Korean Patent Application No. 2007-28878, filed on Mar. 23, 2007, and Korean Patent Application No. 2007-95490, filed on Sep. 19, 2007, both filed in the Korean Intellectual Property Office, the entire disclosure of each of which is incorporated herein by reference for all purposes.

BACKGROUND

1. Field

The following description relates to a multiple-input multiple-output (MIMO) system, and more particularly, to a codebook of precoding matrices for use in MIMO systems and a method of generating a codebook for use in such MIMO systems.

2. Description of the Related Art

Currently, wireless communication technologies for providing a variety of multimedia services in wireless communication environments are expanding. High-speed data transmission is needed to provide high quality multimedia services in wireless communication systems. Accordingly, various research has been conducted to support high-speed data transmission in such wireless communication systems. A recent proposal to achieve high-speed data transmission relates to the use of multiple antennas at both the transmitter and the receiver, known as multiple-input multiple-output (MIMO) systems.

MIMO technology offers significant increases in channel capacities with limited frequency resources and in data transmission rates by using multiple antennas at both the transmitter and the receiver. In such MIMO systems, a number of antennas are used when scattering conditions are substantial, and theoretically, MIMO systems provide channel capacities proportional to the number of antennas. Such MIMO technology can serve as an important component of the next generation mobile communication systems, such as 3^(rd) Generation Partnership Project (3GPP), Super 3G (or 3G Long Term Evolution “LTE”), 3GPP2 and upcoming 4G systems, particularly, for the downlink from a single base station to multiple user equipments.

However, when MIMO technology is deployed, the physical space and area for installing antennas may be limited. Communication systems using MIMO technology are highly affected by spacing between antennas. Specifically, as the spacing between antennas becomes smaller, higher correlation between wireless channels can be generated. Particularly, when antennas have the same polarization, higher correlation between wireless channels can be generated. Correlation generated between wireless channels reduces reliability for data communication and also reduces data transmission rates.

Accordingly, various methods of using the polarization direction of antennas are needed in order to reduce an area for installing multiple antennas and also to increase channel capacities. When multi-polarized antennas are used in MIMO systems, Correlation between wireless channels can be reduced.

Coding operations, referred to as a precoding, are needed to effectively transmit data, via wireless channels, in MIMO systems to maximize system performance and capacity. Precoding represents multi-layer beamforming in which a transmission signal (data) is emitted from each of the antennas in accordance with a data precoding rule, i.e., appropriate phase (and gain) weighting such that the signal power is maximized at the receiver input and the multipath fading effect is minimized. The weight can be expressed in terms of a precoding matrix (i.e., a set of beam-forming vectors) and is selected from a set of precoding matrices in a codebook.

Currently, there are various types of codebooks designed for the particular cases of single-polarized MIMO schemes where the polarization of antennas is single-polarization. However, no effective codebook has been offered in association with cases of multi-polarized MIMO schemes where the polarization of antennas is multi-polarization. Existing codebooks designed for single-polarized MIMO schemes cannot be optimized for multi-polarized MIMO schemes.

Accordingly, there is a need for a method and apparatus for generating a codebook for a MIMO system with low complexity and excellent performance, even when the polarization of antennas is multi-polarization.

SUMMARY

In one general aspect, there is provided a communication apparatus for a communication between a transmitter having eight transmit antennas and a receiver having at least one receive antenna, the communication apparatus including: a codebook storage unit configured to store at least one matrix W_(i) including eight rows, where i is a natural number, and a precoder configured to precode a data stream desired to be transmitted based on one of the stored at least one matrix W_(i), wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), includes a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, includes the zero matrix.

The communication apparatus may further include: an information receiver configured to receive information associated with a matrix selected by the receiver from the stored at least one matrix W_(i), wherein the precoder is further configured to precode the data stream based on a precoding matrix generated based on information associated with the selected matrix.

In the communication apparatus, each of the at least one matrix W_(i) may include: a transmission rank of 2, and a dimension of 8×2.

In another general aspect, there is provided a communication apparatus, including: a codebook configured to be used for a communication between a transmitter including eight transmit antennas and a receiver including at least one receive antenna, the codebook including at least one matrix W_(i) including eight rows, i being a natural number, each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), including a nonzero matrix, the nonzero matrix excluding a zero matrix, each remaining block, excluding the diagonal blocks, including the zero matrix.

In the communication apparatus, each of the at least one matrix W_(i) may include: a transmission rank of 2, and a dimension of 8×2.

In another general aspect, there is provided a communication apparatus for a communication between a transmitter including eight transmit antennas and a receiver including at least one receive antenna, the communication apparatus including: a codebook storage unit configured to store at least one matrix W_(i), where i is a natural number, a selector configured to select, as a target matrix, one of the stored at least one matrix W_(i), and an information feedback unit configured to feed back information associated with the target matrix to the transmitter, wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), includes a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, includes the zero matrix.

In the communication apparatus, the selector may be further configured to select the target matrix in response to a pilot signal transmitted from the transmitter.

In the communication apparatus, the information feedback unit may be further configured to feed back index information of the target matrix.

In another general aspect, there is provided a communication method for a communication between a transmitter including eight transmit antennas and a receiver including at least one receiver, the communication method including: generating a precoding matrix based on one of at least one pre-stored matrix W_(i) including eight rows, where i is a natural number, and precoding a data stream desired to be transmitted based on the one of at least one matrix W_(i), wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), includes a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, includes the zero matrix.

The communication method may further include: receiving, by a receiver, information associated with a matrix selected by the receiver from the stored at least one matrix W_(i), and precoding the data stream based on a precoding matrix generated based on information associated with the selected matrix.

In the communication apparatus, each of the at least one matrix W_(i) may include: a transmission rank of 2, and a dimension of 8×2.

In another general aspect, there is provided a communication method for a communication between a transmitter including eight transmit antennas and a receiver including at least one receive antenna, the communication method including: selecting, as a target matrix, one of pre-stored at least one matrix W_(i), where i is a natural number, and feeding back information associated with the target matrix to the transmitter, wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), includes a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, includes the zero matrix.

In the communication method, each of the at least one matrix W_(i) may include: a transmission rank of 2, and a dimension of 8×2.

In another general aspect, there is provided a communication method for a communication between a transmitter including eight transmit antennas and a receiver including at least one receive antenna, the communication method including: storing at least one matrix W_(i), where i is a natural number, selecting, as a target matrix, one of the stored at least one matrix W_(i), and feeding back information associated with the target matrix to the transmitter, wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), includes a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, includes the zero matrix.

The communication method may further include selecting the target matrix in response to a pilot signal transmitted from the transmitter.

The communication method may further include feeding back index information of the target matrix.

In the communication method, the feedback may start initially and restarts periodically, by sending a one-shot feedback that fully depicts the precoder by itself.

In the communication method, the feedback may start initially and restarts periodically, by sending a one-shot feedback that fully depicts the precoder by itself.

The communication method may further include starting the feedback initially and restarting the feedback periodically, by sending a one-shot feedback that fully depicts a precoder by itself.

The communication method may further include starting the feedback initially and restarting the feedback periodically, by sending a one-shot feedback that fully depicts a precoder by itself.

The communication method may further include starting the feedback initially and restarting the feedback periodically, by sending a one-shot feedback that fully depicts a precoder by itself.

In the communication method, a total number of bits of fed back may be 120.

In the communication method, a total number of bits of fed back may be 120.

A non-transitory computer-readable medium may include a program to instruct a computer to implement any of the above methods.

Other features and aspects may be apparent from the following detailed description, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C illustrate multi-polarized transmitting/receiving antennas in a MIMO system according to example embodiments.

FIG. 2 is a flowchart illustrating a method of generating a codebook of precoding matrices for use in a multi-polarized MIMO system according to an example embodiment.

FIG. 3 illustrates a precoding matrix for use in a multi-polarized MIMO system according to an example embodiment.

FIG. 4 illustrates precoding matrices where a discrete Fourier transform (DFT) precoding matrix is assigned to diagonal blocks in a multi-polarized MIMO system according to an example embodiment.

FIG. 5 is a block diagram illustrating a codebook generation apparatus for generating a codebook of precoding matrices for use in a multi-polarized MIMO system according to an example embodiment.

Throughout the drawings and the detailed description, unless otherwise described, the same drawing reference numerals will be understood to refer to the same elements, features, and structures. The relative size and depiction of these elements may be exaggerated for clarity, illustration, and convenience.

DETAILED DESCRIPTION

The following detailed description is provided to assist the reader in gaining a comprehensive understanding of the methods, apparatuses, and/or systems described herein. Accordingly, various changes, modifications, and equivalents of the systems, apparatuses and/or methods described herein will be suggested to those of ordinary skill in the art. The progression of processing steps and/or operations described is an example; however, the sequence of steps and/or operations is not limited to that set forth herein and may be changed as is known in the art, with the exception of steps and/or operations necessarily occurring in a certain order. Also, descriptions of well-known functions and constructions may be omitted for increased clarity and conciseness.

Prior to describing embodiments in detail, examples of current codebooks designed for single-polarized MIMO including a discrete Fourier transform (DFT) codebook and a rotated DFT codebook are provided herein below to help understanding the construction of the new codebook for the particular case of multi-polarized MIMO. For example, a DFT codebook providing a DFT precoding matrix for use in a single-polarized MIMO system may be represented as follows in Equation 1.

γ={U⁽⁰⁾, U⁽¹⁾, . . . , U⁽² ^(B) ⁻¹⁾}: Precoding matrix set

U^((b))=[u₀ ^((b)) . . . u_(M-1) ^((b))]: bth precoding matrix

u_(m-1) ^((b)): mth column vector in the matrix U^((b))  [Equation 1]

where B is the number of bits necessary to indicate one of those 2^((B)) DFT precoding matrices, M is a number of transmitting antennas, γ is a DFT codebook that is a set of DFT precoding matrices, and U^((b)) is the b^(th) DFT precoding matrix. The m^(th) column vector in the matrix U^((b)) may be represented as u_(m-1) ^((b)). Specifically, the DFT codebook includes 2^((B)) DFT precoding matrices. Each of the 2^((B)) DFT precoding matrices includes M column vectors.

Also, each of the DFT precoding matrices is an M×M matrix, and u_(m-1) ^((b)) is a vector having m elements and may be a column vector having a size of M×1.

In the DFT codebook, u_(m) ^((b)) may be defined as follows in Equation 2.

$\begin{matrix} {{u_{m}^{(b)} = {\frac{1}{\sqrt{M}}\begin{bmatrix} u_{0{in}}^{(b)} & \cdots & u_{{({M\; 1})}m}^{(b)} \end{bmatrix}}^{T}}{u_{nm}^{(b)} = {\exp \left\{ {j\frac{2\pi \; n}{M}\left( {m + \frac{b}{2^{B}}} \right)} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack \end{matrix}$

That is, 2^((B)) DFT precoding matrices exist in the DFT codebook. Each DFT precoding matrix is an M×M matrix. Also, each of the M×M DFT precoding matrices includes M column vectors. Each column vector may be an M×1 column vector, and elements of the column vector may be determined as in the above Equation 2.

For example, when the polarization of two (2) transmitting antennas are single-polarization, the DFT precoding matrix may include two matrices given as follows in Equation 3.

$\begin{matrix} {\begin{bmatrix} 1 & 1 \\ j & {- j} \end{bmatrix},\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack \end{matrix}$

In contrast to the current DFT codebook for single-polarized MIMO system, a rotated DFT codebook is a set of rotated DFT precoding matrices for use in a single-polarized MIMO system. Such a rotated DFT codebook may be represented as follows in Equation 4.

(E, E², . . . E² ^(B) ): such that U^((s))

E^(s+1)  [Equation 4]

An i^(th) rotated DFT precoding matrix may be represented as follows in Equation 5:

$\begin{matrix} {{E^{(i)} = {\begin{bmatrix} ^{{j\theta}_{0}} & 0 & \cdots & 0 \\ 0 & ^{{j\theta}_{1}} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & ^{{j\theta}_{M - 1}} \end{bmatrix}{DFT}_{M}}},} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack \end{matrix}$

where DFT_(M) is a DFT precoding matrix in the single-polarized MIMO system. The rotated DFT precoding matrix DFT_(M) is generated by rotating all the elements, included in each of rows of the DFT precoding matrix, by a particular phase.

Also, in a MIMO system, a transmitting antenna located at a transmitter side transmits a data signal, via a wireless channel, to a receiving antenna located at a receiver side. The wireless channel may be referred to as a channel matrix H. In a multi-polarized MIMO system, the channel matrix H may be modeled as H=X⊙H′. Here, the symbol “⊙” denotes a Hadamard product of matrices and has a calculation rule, as given by the following Equation 6.

$\begin{matrix} {{\begin{bmatrix} a & b \\ c & d \end{bmatrix} \odot \begin{bmatrix} x & y \\ z & w \end{bmatrix}} = \begin{bmatrix} {ax} & {by} \\ {cz} & {dw} \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack \end{matrix}$

Hereinafter, the embodiments will be described in detail with reference to the accompanying drawings.

Turning now to FIGS. 1A-1C, various combinations of dual-polarized transmitting/receiving antennas for multi-polarized MIMO channels according to example embodiments are illustrated.

Referring to FIG. 1A, a MIMO system 110 includes two transmitting antennas (2Tx) 111 and 112 arranged at a transmitter side, and two receiving antennas (2Rx) 113 and 114 arranged at a receiver side. The two transmitting antennas 111 and 112 are perpendicular to each other. Accordingly, the polarization directions of signals transmitted, via a wireless channel (i.e., channel matrix H), by the transmitting antennas 111 and 112 are orthogonal to each other.

For 2Tx-2Rx: Precoding matrix X may be represented as follows:

$X = \begin{bmatrix} 1 & \sqrt{\chi} \\ \sqrt{\chi} & 1 \end{bmatrix}$

The parameter χ, called “depolarization factor,” can be thought of as a global XPD (cross polarization discrimination) of the antennas and the channel. The exact value of the depolarization factor can be difficult to quantify as it depends upon many factors and will vary from one wireless environment to another. Such a depolarization factor can cover the wide range of values of values 0≦χ≦1.

Similarly, another MIMO system 120, as shown in FIG. 1B, includes four transmitting antennas (4Tx) 121, 122, 123, and 124 arranged at a transmitter side, and two receiving antennas (2Rx) 125 and 126 arranged at a receiver side. The polarized directions of signals transmitted, via a wireless channel (i.e., channel matrix H), by two transmitting antennas 121 and 122 and remaining two transmitting antennas 123 and 124 are orthogonal to each other.

For 4Tx-2Rx: Precoding matrix X may be represented as follows:

$X = \begin{bmatrix} 1 & 1 & \sqrt{\chi} & \sqrt{\chi} \\ \sqrt{\chi} & \sqrt{\chi} & 1 & 1 \end{bmatrix}$

Also, still another MIMO system 130, as shown in FIG. 10, includes four transmitting antennas (4Tx) 131, 132, 133, and 134 arranged at a transmitter side, and four receiving antennas (4Rx) 135, 136, 137, and 138 arranged at a receiver side.

For 4Tx-4Rx: Precoding matrix X may be represented as follows in Equation 7.

$\begin{matrix} {X = \begin{bmatrix} 1 & 1 & \sqrt{\chi} & \sqrt{\chi} \\ 1 & 1 & \sqrt{\chi} & \sqrt{\chi} \\ \sqrt{\chi} & \sqrt{\chi} & 1 & 1 \\ \sqrt{\chi} & \sqrt{\chi} & 1 & 1 \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack \end{matrix}$

where χ is a real number, and 0≦χ≦1.

Referring to Equation 7, the first column and the second column of the matrix X correspond to two transmitting antennas (2Tx) 121 and 122, and the third column and the fourth column of the matrix X correspond to other two transmitting antennas (2Tx) 123 and 124.

Specifically, the channel matrix H may be modeled as: H=X⊙H′. Also, when four transmitting antennas (4Tx) and four receiving antennas (4Rx) are arranged in the MIMO system 130, shown in FIG. 1C, the precoding matrix X may be a 4×4 matrix, as shown in Equation 7. Also, the four transmitting antennas (4Tx) 131, 132, 133, and 134 transmit signals in two polarization directions. As a result, the matrix X may be modeled as a precoding matrix having the two blocks in a diagonal direction.

When a distance between transmitting antennas (Tx) and receiving antennas (Rx) is small, that is, for example, when the user equipment (UE) is close to the base station (BS), parameter χ, called depolarization factor, may be modeled close to zero “0”. Conversely, when a distance between transmitting antennas (Tx) and receiving antennas (Rx) is great, that is, for example, when there are large cells within the wireless networks, χ may be modeled close to one “1”. Accordingly, when χ changes from “0” to “1”, that is, within the range of 0≦χ≦1, the codebook should have excellent performance in both a single-polarized MIMO system and a multi-polarized MIMO system.

FIG. 2 is a flowchart illustrating a method of generating a codebook for use in a multi-polarized MIMO system according to an example embodiment. Such a codebook is provided with a set of unitary matrices designed not only for multi-polarized MIMO schemes, but also single-polarized MIMO schemes without any significant performance degradation. The codebook for such multi-polarized MIMO can be constructed in a block diagonal structure, known as a block diagonal multi-polarized codebook. Similarly, a precoding matrix for use in a multi-polarized MIMO in such a block diagonal structure can be expressed in terms of M×N, where M indicates a number of transmitting antennas at a transmitter side and N indicates a number of data streams in the matrix X. The size of such a matrix may be determined according to a transmission rank (spatial multiplexing rate) corresponding to at least one of the number of transmitting antennas and the number of data streams to be transmitted, via the wireless channels. For example, if the number of transmitting antennas (Tx) is four (4) and the transmission rank, that is, the number of data streams is also four (4), then the size of the matrix may be 4×4.

Such a matrix (block diagonal multi-polarized codebook) may be organized or modeled as having a plurality of blocks according to a number of polarization directions of transmitting antennas within a block diagonal structure. Blocks in a diagonal direction are known as diagonal blocks. In an M×N matrix, the term “diagonal direction” refers to a direction from an element of a first column and a first row to an element in an M^(th) column and N^(th) row. For example, when a 4×4 matrix is divided into four sets of 2×2 matrices, a 2×2 matrix that includes elements, included in either the first (1st) or second (2^(nd)) column and also included in either the first (1st) or second (2^(nd)) row of the matrix, and another 2×2 matrix that includes elements, included in either the third (3rd) or fourth (4^(th)) column and also included in either the third (3rd) or fourth (4^(th)) row of the matrix, are characterized as “diagonal blocks.”

In this instance, when the number of polarization directions of transmitting antennas is two (2), the total number of diagonal blocks may be two (2) and the total number of remaining blocks within the block diagonal structure may be two (2). Similarly, when the number of polarization directions of transmitting antennas is three (3), the total number of diagonal blocks may be three (3) and the total number of remaining blocks may be six (6).

Referring to FIG. 2, in operation S210, a single-polarized precoding matrix is assigned to each of diagonal blocks among a plurality of blocks within the diagonal block structure. Such a single-polarized precoding matrix is a precoding matrix designed for single-polarized MIMO.

For example, the single-polarized precoding matrix assigned to the diagonal blocks in such a block diagonal multi-polarized codebook may include a DFT precoding matrix or a rotated DFT precoding matrix selected in a matrix codebook designed for single-polarized MIMO, e.g., the DFT codebook or the rotated DFT codebook or any other matrix codebook. Any one of the DFT precoding matrix and the rotated DFT precoding matrix may be assigned to diagonal blocks.

In addition, the size of the single-polarized precoding matrix may be determined according to the number of transmitting antennas (Tx) having the same polarization direction. For example, it is assumed that the total number of transmitting antennas (Tx) is eight (8), and the polarization direction by two transmitting antennas (2Tx) is a direction x and the polarization direction by the remaining six transmitting antennas (6Tx) is a direction y. In this case, the direction x is perpendicular to the direction y. Also, the number of polarization directions is two (2), that is, the directions x and y. Accordingly, the precoding matrix for multi-polarized MIMO may have two diagonal blocks.

Also, the number of rows of the single-polarized precoding matrix that are assigned to one diagonal block may be six (6) and the number of rows of the single-polarized precoding matrix that are assigned to the remaining one diagonal block may be two (2). In this case, if the transmission rank is eight (8), more specifically, if the transmission rank of two antennas having the direction x as the polarization direction is two (2) and the transmission rank of six antennas having the direction y as the polarization direction is six (6), a 2×2 single-polarized precoding matrix may be assigned to any one of two diagonal blocks and a 6×6 single-polarized precoding matrix may be assigned to the other one of the two diagonal blocks.

In operation S220, a zero matrix is assigned to each of the remaining blocks, excluding the diagonal blocks, within the block diagonal structure.

Specifically, the zero matrix of which all the elements are ‘0’ is assigned to blocks that are not the diagonal blocks among the blocks that are obtained within the block diagonal structure according to the number of polarization directions of transmitting antennas.

In operation S230, a precoding matrix for multi-polarized MIMO, i.e., a block diagonal multi-polarized codebook is then generated by combining the single-polarized precoding matrices assigned to the diagonal blocks and the zero matrices assigned to the remaining blocks within the block diagonal structure.

For example, if four transmitting antennas (4Tx) exist, and two transmitting antennas (2Tx) thereof have the direction x as the polarization direction and the remaining two transmitting antennas (2Tx) have the direction y as the polarization direction, the codebook for the multi-polarized MIMO system may include a 4×4 matrix as provided, for example, by Equation 8.

$\begin{matrix} {\begin{bmatrix} 1 & 1 & 0 & 0 \\ j & {- j} & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & j & {- j} \end{bmatrix},\begin{bmatrix} 1 & 1 & 0 & 0 \\ 1 & {- 1} & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & {- 1} \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \end{matrix}$

The two multi-polarized precoding matrices of Equation 8 are only an example embodiment. Multi-polarized precoding matrices may be generated by randomly combining the two DFT precoding matrices of Equation 3, for example, assigned to the diagonal blocks with the two zero matrices assigned to the remaining blocks within the block diagonal structure.

Specifically, the precoding matrix for the multi-polarized MIMO system may be generated by organizing the precoding matrix into the plurality of blocks according to the number of polarization directions of transmitting antennas, and assigning the single-polarized precoding matrix to the diagonal blocks among all blocks. The zero matrix is then assigned to each of the remaining blocks within the block diagonal structure.

For example, when it is assumed that four transmitting antennas exist and the number of polarization directions of transmitting antennas is two (2), the size of the precoding matrix for multi-polarized MIMO may be 4×4. Also, since the number of polarization directions of transmitting antennas is two (2), the precoding matrix may be organized into a total of four (4) blocks according to the number of polarization directions. The precoding matrix for multi-polarized MIMO (block diagonal multi-polarized codebook) is then generated by assigning the single-polarized precoding matrix to each of the two (2) diagonal blocks and assigning the zero matrix to each of the two (2) remaining blocks that are not the two (2) diagonal blocks within the block diagonal structure.

In operation S240, the precoding matrix (block diagonal multi-polarized codebook) is then reconstructed by selecting, from the same precoding matrix, at least one column vector according to a transmission rank corresponding to a number of data streams to be transmitted, via the wireless channel.

For example, it may be assumed that if four transmitting antennas have a multi polarization, a 4×4 precoding matrix is generated. The 4×4 precoding matrix is given by Equation 9.

$\begin{matrix} \begin{bmatrix} 1 & 1 & 0 & 0 \\ 1 & {- 1} & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & {- 1} \end{bmatrix} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack \end{matrix}$

Referring to Equation 9, when the transmission rank is two (2), the precoding matrix (block diagonal multi-polarized codebook) may be reconstructed by selecting two column vectors from four column vectors included in the precoding matrix. Specifically, the precoding matrix of Equation 9 may be reconstructed to generate six precoding matrices having a size of 4×2, as given by Equation 10.

$\begin{matrix} {\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \\ 0 & 0 \\ 0 & 0 \end{bmatrix},\begin{bmatrix} 0 & 0 \\ 0 & 0 \\ 1 & 1 \\ 1 & {- 1} \end{bmatrix},\begin{bmatrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{bmatrix},\begin{bmatrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & {- 1} \end{bmatrix},\begin{bmatrix} 1 & 0 \\ {- 1} & 0 \\ 0 & 1 \\ 0 & 1 \end{bmatrix},{\quad\begin{bmatrix} 1 & 0 \\ {- 1} & 0 \\ 0 & 1 \\ 0 & {- 1} \end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack \end{matrix}$

When the number of transmitting antennas is M and the transmission rank is r, an M×M precoding matrix may be generated. Also, an M×r precoding matrix may be generated by selecting column vectors according to the transmission rank and reconstructing the precoding matrix.

Specifically, according to an embodiment, unnecessary column vectors may be removed from the precoding matrix by reconstructing the precoding matrix according to the transmission rank, and thus a codebook may be efficiently generated.

In operation S250, when the polarization direction of transmitting antennas is rotated, a rotated precoding matrix is generated using the precoding matrix and a rotated matrix. The rotated matrix may correspond to a rotated angle of polarization direction of transmitting antennas (Tx).

The array structure of transmitting antennas may be variously embodied. For example, in the multi-polarized MIMO system, transmitting antennas corresponding to one polarization direction may be installed vertically with respect to a reference plane and transmitting antennas corresponding to another polarization direction may be installed horizontally with respect to the reference plane. Also, the transmitting antennas corresponding to one polarization direction may be installed in a direction of +45 degrees with respect to the reference plane and transmitting antennas corresponding to the other polarization direction may be installed in a direction of −45 degrees with respect to the reference plane.

Specifically, when the polarization direction of transmitting antennas is rotated by a particular angle with respect to the reference plane, a data stream must be beam formed using the rotated precoding matrix. The rotated precoding matrix may be generated by rotating the precoding matrix. Specifically, the rotated precoding matrix may be generated by multiplying the precoding matrix and the rotated matrix.

For example, when it is assumed that respective two transmitting antennas among four transmitting antennas are installed in a direction of +45 degrees and in a direction of −45 degrees with respect to the reference plane, the rotated matrix may be represented as follows in Equation 11.

$\begin{matrix} {U_{rot} = \begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack \end{matrix}$

The rotated matrix U_(rot) may be multiplied by a random complex value. The resulting structure when multiplying the rotated matrix U_(rot) by the random scalar value falls within the scope of embodiments.

When the precoding matrix is referred to as W_(BD), the rotated precoding matrix W_(RBD) that is generated by rotating the precoding matrix W_(BD) may be represented as follows in Equation 12.

$\begin{matrix} {W_{RBD} = {\frac{1}{2}U_{rot}W_{BD}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack \end{matrix}$

Referring to Equation 12, the rotated matrix U_(rot) may be determined to correspond to the rotated angle of polarization direction of transmitting antennas.

According to an embodiment, even when various types of arrays are provided, such as transmitting antennas with a rotated polarization direction, the rotated precoding matrix may be readily generated using the rotated matrix.

In operation S250, a reordered matrix is obtained by reordering column vectors that are included in the precoding matrix, and the reordered matrix and the rotated matrix are used to generate a rotated precoding matrix.

For example, it is assumed that when two respective transmitting antennas among four transmitting antennas are installed in a direction of +45 degrees and in a direction of −45 degrees with respect to the reference plane, the precoding matrix W_(BD) is generated. In this instance, the rotated matrix U_(rot), is the same as Equation 11. The precoding matrix W_(BD) is represented as follows in Equation 13:

$\begin{matrix} {W_{BD} = \begin{bmatrix} 1 & 1 & 0 & 0 \\ {- 1} & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & {- 1} & 1 \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack \end{matrix}$

When column vectors included in the precoding matrix W_(BD) of Equation 13 are reordered, the reordered matrix W_(reorder,BD) may be represented as follows in Equation 14.

$\begin{matrix} {W_{{reorder},{BD}} = \begin{bmatrix} 1 & 0 & 1 & 0 \\ {- 1} & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & {- 1} & 0 & 1 \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack \end{matrix}$

By using the reordered matrix W_(reorder,BD) and the rotated matrix U_(rot) of Equation 11, the rotated precoding matrix W_(RBD) may be generated and a data stream may be beam formed using the rotated precoding matrix W_(RBD), represented as follows in Equation 15.

$\begin{matrix} \begin{matrix} {W_{RBD} = {\frac{1}{2}U_{rot}W_{BD}}} \\ {= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 1 & 0 & 1 & 0 \\ {- 1} & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & {- 1} & 0 & 1 \end{bmatrix}}} \\ {= {\frac{1}{2}\begin{bmatrix} 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 \end{bmatrix}}} \end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack \end{matrix}$

Referring to Equation 15, it may be seen that when two respective transmitting antennas among four transmitting antennas are installed in a direction of +45 degrees and in a direction of −45 degrees with respect to the reference plane, the rotated precoding matrix W_(RBD) corresponding to the precoding matrix W_(BD) of Equation 13 may be generated like Equation 15.

In operation S260, a phase of each of elements included in the reordered matrix is adjusted. The phase of each of elements included in the reordered matrix may be adjusted using a diagonal matrix. In this instance, the diagonal matrix includes diagonal elements. Also, the phase of each of the diagonal elements may be the same or different from each other. The amplitude of each diagonal element is set to ‘1’. The amplitude of each of remaining elements, excluding the diagonal elements, is set to ‘0’.

The diagonal matrix is associated with a modulation scheme of data symbols, instead of increasing channel capacities of the MIMO system, and the like. For example, when the data symbol is modulated using quadrature phase shift keying (QPSK), the diagonal matrix may change only the phase of the data symbol, but may not affect channel capacities of the MIMO system.

In this instance, it is assumed that the precoding matrix W_(BD) and the reordered matrix W_(reorder,BD) are given by Equation 16.

$\begin{matrix} {W_{BD} = {{\begin{bmatrix} 1 & 1 & 0 & 0 \\ j & {- j} & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & j & {- j} \end{bmatrix}W_{{recorder},\; {BD}}} = \begin{bmatrix} 1 & 0 & 1 & 0 \\ j & 0 & {- j} & 0 \\ 0 & 1 & 0 & 1 \\ 0 & j & 0 & {- j} \end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack \end{matrix}$

In this instance, the phase of each element included in the reordered matrix W_(reorder,BD) may be adjusted like Equation 17 below, and data symbols may be beam formed by using W′_(reorder,BD).

$\begin{matrix} \begin{matrix} {W_{{reorder},{BD}}^{\prime} = {W_{{reorder},{BD}}\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & j & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & j \end{bmatrix}}} \\ {= \begin{bmatrix} 1 & 0 & 1 & 0 \\ j & 0 & {- j} & 0 \\ 0 & j & 0 & j \\ 0 & {- 1} & 0 & 1 \end{bmatrix}} \end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack \end{matrix}$

The processes, functions, methods and/or software described herein may be recorded, stored, or fixed in one or more computer-readable storage media that includes program instructions to be implemented by a computer to cause a processor to execute or perform the program instructions. The media may also include, alone or in combination with the program instructions, data files, data structures, and the like. The media and program instructions may be those specially designed and constructed, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable media include magnetic media, such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM disks and DVDs; magneto-optical media, such as optical disks; and hardware devices that are specially configured to store and perform program instructions, such as read-only memory (ROM), random access memory (RAM), flash memory, and the like. Examples of program instructions include machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. The described hardware devices may be configured to act as one or more software modules in order to perform the operations and methods described above, or vice versa. In addition, a computer-readable storage medium may be distributed among computer systems connected through a network and computer-readable codes or program instructions may be stored and executed in a decentralized manner.

FIG. 3 illustrates a precoding matrix for use in a multi-polarized MIMO system according to an example embodiment.

Referring to FIG. 3, when the number of transmitting antennas is four (4) and the number of polarization directions of transmitting antennas is two (2), U indicates a precoding matrix for the multi-polarized MIMO system. Matrices such as an ‘A’ matrix 310 and a ‘B’ matrix 320, as shown in FIG. 3, indicate a single-polarized precoding matrix, that is, a precoding matrix selected from a matrix codebook designed for single-polarized MIMO, e.g., DFT codebook or rotated DFT codebook or any other matrix codebook, and two ‘O’ matrices 330 and 340 indicate zero matrices.

Since the number of polarization directions of transmitting antennas is two (2), two diagonal blocks and two remaining blocks exist. The ‘A’ matrix 310 and the ‘B’ matrix 320, that is, single-polarized precoding matrices, are assigned to the diagonal blocks respectively. The ‘O’ matrices 330 and 340, that is, zero matrices, are assigned to the remaining blocks respectively.

The size of the ‘A’ matrix 310 and the ‘B’ matrix 320 may be determined according to the number of transmitting antennas having the same polarization direction.

For example, when the polarization directions of transmitting antennas are a direction x and a direction y, the number of polarization directions of transmitting antennas may be two (2). Also, it may be assumed that when a total number of transmitting antennas is four (4), the polarization direction of two transmitting antennas is the direction x and the polarization direction of the remaining two transmitting antennas is the direction y. In this instance, the ‘A’ matrix 310 may be a single-polarized precoding matrix corresponding to the polarization direction of the direction x. Since the number of transmitting antennas having a polarization direction in the direction x is two (2), the number of rows of the ‘A’ matrix 310 may be two (2). Also, the number of rows of the ‘B’ matrix 320 may be two (2).

When the transmission rank for the direction x is two (2), the number of rows of the ‘A’ matrix 310 may be two (2). Also, when the transmission rank for the direction y is two (2), the number of rows of the ‘B’ matrix 320 may be two (2).

FIG. 4 illustrates single-polarized precoding matrices, such as, DFT precoding matrices assigned to diagonal blocks in a multi-polarized MIMO system according to an example embodiment.

Referring to FIG. 4, W_(BD,1) and W_(BD,2) are precoding matrices when the number of transmitting antennas is four (4), the number of polarization directions of transmitting antennas is two (2), and the number of transmitting antennas having the same polarization direction is two (2).

The DFT precoding matrices that are assigned to diagonal blocks of the precoding matrices W_(BD,1) and W_(BD,2) can be represented as follows in Equation 18.

$\begin{matrix} {\begin{bmatrix} 1 & 1 \\ 1 & {- 1} \end{bmatrix},\begin{bmatrix} 1 & 1 \\ j & {- j} \end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack \end{matrix}$

An example of reordered matrices W_(reorder,BD,1), W_(reorder,BD,2), W_(reorder,BD,3), W_(reorder,BD,4), W_(reorder,BD,5)) W_(reorder,BD,5), W_(reorder,BD,7), and W_(reorder,BD,8) that are generated by reordering column vectors included in the precoding matrices W_(BD,1) and W_(BD,2) may be represented as follows in Equation 19.

$\begin{matrix} {{W_{{reorder},{BD},1} = \begin{bmatrix} 1 & 0 & 1 & 0 \\ 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & {- 1} \end{bmatrix}},{W_{{reorder},{BD},2} = \begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 1 & 0 & {- 1} & 0 \end{bmatrix}},{W_{{reorder},{BD},3} = \begin{bmatrix} 1 & 0 & 1 & 0 \\ j & 0 & {- j} & 0 \\ 0 & 1 & 0 & 1 \\ 0 & j & 0 & {- j} \end{bmatrix}},{W_{{reorder},{BD},4} = \begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & {- j} & 0 & j \\ 1 & 0 & 1 & 0 \\ {- j} & 0 & j & 0 \end{bmatrix}},{W_{{reorder},{BD},5} = \begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & j & 0 & {- j} \\ 1 & 0 & 1 & 0 \\ j & 0 & {- j} & 0 \end{bmatrix}},{W_{{reorder},{BD},6} = \begin{bmatrix} 1 & 0 & 1 & 0 \\ {- 1} & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & {- 1} & 0 & 1 \end{bmatrix}},{W_{{reorder},{BD},7} = \begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & {- 1} & 0 & 1 \\ 1 & 0 & 1 & 0 \\ {- 1} & 0 & 1 & 0 \end{bmatrix}},{W_{{reorder},{BD},8} = \begin{bmatrix} 1 & 0 & 1 & 0 \\ {- j} & 0 & j & 0 \\ 0 & 1 & 0 & 1 \\ 0 & {- j} & 0 & j \end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack \end{matrix}$

The reordered matrices may be multiplied by a diagonal matrix. In this instance, diagonal elements of the diagonal matrix are complex numbers that have the size of 1, and remaining elements are 0. The diagonal matrix does not affect channel capacities or beam forming performance, and is associated with a modulation scheme of data symbols.

For example, the phase of each element included in the reordered matrices using random diagonal matrices may be adjusted as shown in Equation 20. In this instance, diagonal elements of a diagonal matrix D_(i) may be random complex numbers that have the magnitude 1.

$\begin{matrix} {\begin{matrix} {W_{C,1} = {W_{{reorder},{BD},1}D_{1}}} \\ {{= {\begin{bmatrix} 1 & 0 & 1 & 0 \\ 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & {- 1} \end{bmatrix}\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & {- 1} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & {- 1} \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{C,2} = {W_{{reorder},{BD},2}D_{2}}} \\ {{= {\begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 1 & 0 & {- 1} & 0 \end{bmatrix}\begin{bmatrix} {- 1} & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & {- 1} \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{C,3} = {W_{{reorder},{BD},3}D_{3}}} \\ {{= {\begin{bmatrix} 1 & 0 & 1 & 0 \\ j & 0 & {- j} & 0 \\ 0 & 1 & 0 & 1 \\ 0 & j & 0 & {- j} \end{bmatrix}\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & j & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & j \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{C,4} = {W_{{reorder},{BD},4}D_{4}}} \\ {{= {\begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & {- j} & 0 & j \\ 1 & 0 & 1 & 0 \\ {- j} & 0 & j & 0 \end{bmatrix}\begin{bmatrix} {- 1} & 0 & 0 & 0 \\ 0 & j & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & {- j} \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{C,5} = {W_{{reorder},{BD},5}D_{5}}} \\ {{= {\begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & j & 0 & {- j} \\ 1 & 0 & 1 & 0 \\ j & 0 & {- j} & 0 \end{bmatrix}\begin{bmatrix} {- 1} & 0 & 0 & 0 \\ 0 & {- j} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & j \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{C,6} = {W_{{reorder},{BD},6}D_{6}}} \\ {{= {\begin{bmatrix} 1 & 0 & 1 & 0 \\ {- 1} & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & {- 1} & 0 & 1 \end{bmatrix}\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{C,7} = {W_{{reorder},{BD},7}D_{7}}} \\ {{= {\begin{bmatrix} 0 & 1 & 0 & 1 \\ 0 & {- 1} & 0 & 1 \\ 1 & 0 & 1 & 0 \\ {- 1} & 0 & 1 & 0 \end{bmatrix}\begin{bmatrix} {- 1} & 0 & 0 & 0 \\ 0 & {- 1} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{C,8} = {W_{{reorder},{BD},8}D_{8}}} \\ {= {\begin{bmatrix} 1 & 0 & 1 & 0 \\ {- j} & 0 & j & 0 \\ 0 & 1 & 0 & 1 \\ 0 & {- j} & 0 & j \end{bmatrix}\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & {- j} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & {- j} \end{bmatrix}}} \end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack \end{matrix}$

Also, a rotated precoding matrix W_(RBD,i) may be generated from W_(C,i) that is generated using the reordered matrix W_(reorder,BD,i) and the diagonal matrix D_(i). More specifically, the rotated precoding matrix W_(RBD,i) may be generated through a mathematical transformation of the precoding matrices W_(BD,1) and W_(BD,2.)

In this instance, when a reordered matrix is generated from the precoding matrix, and W_(C,i) is generated by multiplying the reordered matrix and the diagonal matrix, the rotated precoding matrix W_(RBD,i) may be given by Equation 21.

$\begin{matrix} {W_{{RBD},i} = {\frac{1}{2}U_{rot}W_{C,i}}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack \end{matrix}$

By using Equation 21, the rotated precoding matrix W_(RBD,i) with respect to W_(C,i) included in Equation 20 may be represented as follows in Equation 22.

$\begin{matrix} {\begin{matrix} {W_{{RBD},1} = {\frac{1}{2}U_{rot}W_{C,1}}} \\ {{= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 1 & 0 & 1 & 0 \\ 1 & 0 & {- 1} & 0 \\ 0 & {- 1} & 0 & {- 1} \\ 0 & {- 1} & 0 & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},2} = {\frac{1}{2}U_{rot}W_{C,2}}} \\ {{= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 0 & 1 & 0 & {- 1} \\ 0 & 1 & 0 & 1 \\ {- 1} & 0 & 1 & 0 \\ {- 1} & 0 & {- 1} & 0 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},3} = {\frac{1}{2}U_{rot}W_{C,3}}} \\ {{= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 1 & 0 & 1 & 0 \\ j & 0 & {- j} & 0 \\ 0 & j & 0 & j \\ 0 & {- 1} & 0 & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},4} = {\frac{1}{2}U_{rot}W_{C,4}}} \\ {= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 0 & j & 0 & {- j} \\ 0 & 1 & 0 & 1 \\ {- 1} & 0 & 1 & 0 \\ j & 0 & j & 0 \end{bmatrix}}} \end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack \end{matrix}$

Referring to Equation 22, when transmitting antennas corresponding to one polarization direction are installed in a direction of +45 degrees with respect to the reference plane and transmitting antennas corresponding to another polarization direction are installed in a direction of −45 degrees with respect to the reference plane, four (4) rotated precoding matrices may be generated using the rotated matrix. In this instance, although four rotated precoding matrices are expressed in Equation 22, it will be apparent to those of ordinary skills in the art that various types of rotated precoding matrices may be generated using the technical spirits of embodiments.

Also, the rotated precoding matrix W_(RBD,i) may be represented as follows in Equation 23.

$\begin{matrix} {\begin{matrix} {W_{{RBD},5} = {\frac{1}{2}U_{rot}W_{C,5}}} \\ {{= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 0 & {- j} & 0 & j \\ 0 & 1 & 0 & 1 \\ {- 1} & 0 & 1 & 0 \\ {- j} & 0 & {- j} & 0 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},6} = {\frac{1}{2}U_{rot}W_{C,6}}} \\ {{= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 1 & 0 & 1 & 0 \\ {- 1} & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & {- 1} & 0 & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},7} = {\frac{1}{2}U_{rot}W_{C,7}}} \\ {{= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 0 & {- 1} & 0 & 1 \\ 0 & 1 & 0 & 1 \\ {- 1} & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},8} = {\frac{1}{2}U_{rot}W_{C,8}}} \\ {= {{\frac{1}{2}\begin{bmatrix} 1 & 0 & {- 1} & 0 \\ 0 & 1 & 0 & {- 1} \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}}\begin{bmatrix} 1 & 0 & 1 & 0 \\ {- j} & 0 & j & 0 \\ 0 & {- j} & 0 & {- j} \\ 0 & {- 1} & 0 & 1 \end{bmatrix}}} \end{matrix}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack \end{matrix}$

When calculating the rotated precoding matrix W_(RBD,i) using Equation 22 and Equation 23, it may be represented as follows in Equation 24.

$\begin{matrix} {\begin{matrix} {W_{{RBD},1} = {\frac{1}{2}U_{rot}W_{C,1}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},2} = {\frac{1}{2}U_{rot}W_{C,2}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},3} = {\frac{1}{2}U_{rot}W_{C,3}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & {- j} & 1 & {- j} \\ j & 1 & {- j} & {- 1} \\ 1 & j & 1 & j \\ j & {- 1} & {- j} & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},4} = {\frac{1}{2}U_{rot}W_{C,4}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & j & {- 1} & {- j} \\ j & 1 & {- j} & 1 \\ {- 1} & {- j} & 1 & j \\ {- j} & 1 & {- j} & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},5} = {\frac{1}{2}U_{rot}W_{C,5}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & {- j} & {- 1} & j \\ j & 1 & j & 1 \\ {- 1} & {- j} & 1 & j \\ {- j} & 1 & {- j} & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},6} = {\frac{1}{2}U_{rot}W_{C,6}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},7} = {\frac{1}{2}U_{rot}W_{C,7}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & 1 & 1 \end{bmatrix}}},} \end{matrix}\begin{matrix} {W_{{RBD},8} = {\frac{1}{2}U_{rot}W_{C,8}}} \\ {{= {\frac{1}{2}\begin{bmatrix} 1 & j & 1 & j \\ {- j} & 1 & j & {- 1} \\ 1 & {- j} & 1 & {- j} \\ {- j} & {- 1} & j & 1 \end{bmatrix}}},} \end{matrix}} & {\left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack \mspace{14mu}} \end{matrix}$

Accordingly, various types of communication apparatuses transmitting/receiving data according to a space-division multiple access (SDMA) scheme can perform communication using at least one of the precoding matrices disclosed in Equation 24. SDMA denotes a technology that enables a base station to transmit (or receive) signal (i.e., at least one data stream) to (or from) multiple users in the same bandwidth and time simultaneously, via multiple antennas in order to maximize a data transmission rate and total capacity. Here, the precoding matrices disclosed in Equation 24 are based on when a transmission rank is 4, but it is possible to generate precoding matrices corresponding to various types of transmission ranks by selecting column vectors of the precoding matrices disclosed in Equation 24.

Also, the base station (BS) and terminals may store the codebook of matrices of Equation 24 in a computer-readable recording medium, etc. When the base station (BS) transmits a pilot signal, each of the terminals may select any one of the stored matrices in response to the pilot signal. In this instance, each of the terminals may select any one matrix based on the state of a wireless channel formed between each of the terminals and the base station, and also may select any one matrix based on an achievable data transmission rate. Also, each of the terminals may select any one color vector from column vectors included in the selected matrix.

Also, the terminals may feed back to the base station information associated with the selected matrix, or information associated with the selected column vector. The information associated with the selected matrix may be index information of the selected matrix and the information associated with the selected column vector may be index information of the selected column vector.

In this instance, the base station (BS) may select any one of the matrices disclosed in Equation 24, as a precoding matrix, based on the information fed back from the terminals. In particular, the base station may select the precoding matrix according to a Per-User Unitary Rate Control (PU2RC) scheme. The base station (BS) may perform precoding (beam-forming) on a data stream to be transmitted, via transmitting antennas, using the selected precoding matrix.

Specifically, a terminal according to an aspect may include a signal receiver to receive a pilot signal transmitted from a base station; a codebook storage unit to store a codebook including at least one W, where i is a natural number of 1 through 8:

${W_{1} = {\frac{1}{2}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}}},\mspace{14mu} {W_{2} = {\frac{1}{2}\begin{bmatrix} 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 \end{bmatrix}}},{W_{3} = {\frac{1}{2}\begin{bmatrix} 1 & {- j} & 1 & {- j} \\ j & 1 & {- j} & {- 1} \\ 1 & j & 1 & j \\ j & {- 1} & {- j} & 1 \end{bmatrix}}},\mspace{14mu} {W_{4} = {\frac{1}{2}\begin{bmatrix} 1 & j & {- 1} & {- j} \\ {- j} & 1 & {- j} & 1 \\ {- 1} & j & 1 & {- j} \\ j & 1 & j & 1 \end{bmatrix}}},{W_{5} = {\frac{1}{2}\begin{bmatrix} 1 & {- j} & {- 1} & j \\ j & 1 & j & 1 \\ {- 1} & {- j} & 1 & j \\ {- j} & 1 & {- j} & 1 \end{bmatrix}}},\mspace{14mu} {W_{6} = {\frac{1}{2}\begin{bmatrix} 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 \end{bmatrix}}},{W_{7} = {\frac{1}{2}\begin{bmatrix} 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & 1 & 1 \end{bmatrix}}},\mspace{14mu} {{W_{8} = {\frac{1}{2}\begin{bmatrix} 1 & j & 1 & j \\ {- j} & 1 & j & {- 1} \\ 1 & {- j} & 1 & {- j} \\ {- j} & {- 1} & j & 1 \end{bmatrix}}};}$

a selector to select a target matrix from the stored at least one W, in response to the pilot signal; and an information feedback unit to feed back information associated with the target matrix to the base station.

For instance, the selector may select the target matrix from the stored codebook including at least one W_(i) based on the state of a wireless channel formed between the terminal and the base station. Also, the selector may select the target matrix from the stored codebook including at least one W_(i) based on an achievable data transmission rate. In addition, the selector may select the target matrix from the stored codebook including at least one W_(i) in response to the pilot signal, and select at least one column vector from column vectors included in the selected target matrix. In this instance, the information feedback unit may feed back to the base station information associated with the selected target matrix and information associated with the selected at least one column vector.

Also, a base station according to an aspect may include a codebook storage unit arranged to store a codebook including at least one W_(i) where i is a natural number of 1 through 8:

${W_{1} = {\frac{1}{2}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & {- 1} & {- 1} \\ 1 & {- 1} & 1 & {- 1} \\ 1 & {- 1} & {- 1} & 1 \end{bmatrix}}},\mspace{14mu} {W_{2} = {\frac{1}{2}\begin{bmatrix} 1 & 1 & {- 1} & {- 1} \\ 1 & 1 & 1 & 1 \\ {- 1} & 1 & 1 & {- 1} \\ {- 1} & 1 & {- 1} & 1 \end{bmatrix}}},{W_{3} = {\frac{1}{2}\begin{bmatrix} 1 & {- j} & 1 & {- j} \\ j & 1 & {- j} & {- 1} \\ 1 & j & 1 & j \\ j & {- 1} & {- j} & 1 \end{bmatrix}}},\mspace{14mu} {W_{4} = {\frac{1}{2}\begin{bmatrix} 1 & j & {- 1} & {- j} \\ {- j} & 1 & {- j} & 1 \\ {- 1} & j & 1 & {- j} \\ j & 1 & j & 1 \end{bmatrix}}},{W_{5} = {\frac{1}{2}\begin{bmatrix} 1 & {- j} & {- 1} & j \\ j & 1 & j & 1 \\ {- 1} & {- j} & 1 & j \\ {- j} & 1 & {- j} & 1 \end{bmatrix}}},\mspace{14mu} {W_{6} = {\frac{1}{2}\begin{bmatrix} 1 & {- 1} & 1 & {- 1} \\ {- 1} & 1 & 1 & {- 1} \\ 1 & 1 & 1 & 1 \\ {- 1} & {- 1} & 1 & 1 \end{bmatrix}}},{W_{7} = {\frac{1}{2}\begin{bmatrix} 1 & {- 1} & {- 1} & 1 \\ {- 1} & 1 & {- 1} & 1 \\ {- 1} & {- 1} & 1 & 1 \\ 1 & 1 & 1 & 1 \end{bmatrix}}},\mspace{14mu} {{W_{8} = {\frac{1}{2}\begin{bmatrix} 1 & j & 1 & j \\ {- j} & 1 & j & {- 1} \\ 1 & {- j} & 1 & {- j} \\ {- j} & {- 1} & j & 1 \end{bmatrix}}};}$

an information receiver arranged to receive information associated with a matrix selected by a terminal from the stored codebook including at least one W_(i); a matrix selector arranged to select a precoding matrix based on information associated with the selected matrix; and a precoder arranged to perform precoding on a data stream to be transmitted using the selected precoding matrix.

In this instance, the information receiver may receive information associated with matrices corresponding to a plurality of terminals, in which the matrices are selected by the plurality of terminals respectively. The matrix selector may then select the precoding matrix based on information associated with the matrices corresponding to the plurality of terminals.

Turning now to FIG. 5, a block diagram of a codebook generation apparatus for generating a codebook of precoding matrices for use in a multi-polarized MIMO system according to an example embodiment is illustrated. Referring to FIG. 5, the codebook generation apparatus includes a single-polarized precoding matrix assignment unit 510, a zero matrix assignment unit 520, a precoding matrix generation unit 530, a precoding matrix reconstruction unit 540, a rotated precoding matrix generation unit 550, and a phase adjustment unit 560.

The single-polarized precoding matrix assignment unit 510 assigns a single-polarized precoding matrix to each of diagonal blocks among a plurality of blocks within a block diagonal structure. The blocks are organized according to a number of polarization directions of transmitting antennas.

The zero matrix assignment unit 520 assigns a zero matrix to remaining blocks excluding the diagonal blocks within the block diagonal structure.

The precoding matrix generation unit 530 generates a precoding matrix for multi-polarized MIMO (i.e., a block diagonal multi-polarized codebook) by combining the single-polarized precoding matrices assigned to the diagonal blocks and the zero matrices assigned to the remaining blocks within the block diagonal structure.

The precoding matrix reconstruction unit 540 reconstructs the precoding matrix by selecting, from the precoding matrix, at least one column vector according to a transmission rank corresponding to a number of data streams to be transmitted.

The rotated precoding matrix generation unit 550 generates a rotated precoding matrix using the precoding matrix and a rotated matrix corresponding to a rotated angle of the polarization direction when the polarization direction of transmitting antennas is rotated.

The rotated precoding matrix generation unit 550 may generate a reordered matrix by reordering column vectors that are included in the precoding matrix, and generates the rotated precoding matrix by using the reordered matrix and the rotated matrix.

The phase adjustment unit 560 adjusts a phase of each of elements included in the reordered matrix using a diagonal matrix.

Descriptions not made in relation to the apparatus of FIG. 5 will be the same as the descriptions made with reference to FIGS. 1 through 4, and thus will be omitted.

Matrices included in a precoding matrix (block diagonal multi-polarized codebook) that is generated according to an aspect will be stored in various types of communication apparatuses and used. For example, a communication apparatus may transmit and receive data in a space division multiple access (SDMA) communication system by using a matrix that is generated according to an aspect. The communication apparatus may include various types of devices for the SDMA communication system, such as a base station, a repeater, a terminal, and the like.

Specifically, a communication apparatus according to an aspect may store a precoding matrix (block diagonal multi-polarized codebook) that is generated by assigning a single-polarized precoding matrix to diagonal blocks among a plurality of blocks within a block diagonal structure that are divided or organized according to the number of polarization directions of transmitting antennas, and assigning a zero matrix to remaining blocks excluding the diagonal blocks within the block diagonal structure.

According to an aspect, the precoding matrix (block diagonal multi-polarized codebook) may be generated by combining the single-polarized precoding matrices assigned at diagonal blocks and the zero matrices assigned at remaining blocks within the block diagonal structure.

Also, a communication apparatus according to an aspect may store a matrix that is reconstructed by selecting, from the precoding matrix, at least one column vector according to a transmission rank corresponding to a number of data streams to be transmitted.

Also, a communication apparatus according to an aspect may store a rotated precoding matrix that is generated using the precoding matrix and a rotated matrix corresponding to a rotated angle of the polarization direction when the polarization direction of transmitting antennas is rotated.

Also, a communication apparatus according to an example embodiment may generate a reordered matrix by reordering column vectors that are included in the precoding matrix, and store a matrix that is generated by using the reordered matrix and the rotated matrix.

When the communication apparatus is a base station (BS) used to support multiple user equipments (UEs) in a wireless network, such as 3GPP, Super 3G (3G Long Term Evolution “LTE”), 3GPP2 and upcoming 4G systems, the base station (BS) may transmit a transmission signal that beam forms a data stream using matrices included in the base station (BS). Specifically, the base station (BS) may include a codebook storage unit that stores a codebook of matrices according to an embodiment and a beamformer that beam forms data streams using the stored matrices.

Conversely, when the communication apparatus is a terminal, the terminal may generate feedback data using matrices selected from a codebook stored in the terminal. The feedback data is used when the base station (BS) performs beam-forming in which multiple data streams are emitted from transmitting antennas in accordance with matrices selected from a codebook stored in the terminal. Specifically, the terminal may include a codebook storage unit that stores a codebook of matrices according to an embodiment and a feedback data generation unit that generates feedback data corresponding to a wireless channel of the base station using the stored matrices.

According to aspects, there is provided a method and apparatus for generating a codebook for a multi-polarized MIMO system that can generate a precoding matrix using a single-polarized precoding matrix even when the polarization of antennas is multi-polarization, and thereby generate an excellent precoding matrix that is easily generated. Such a codebook can be shared by a transmitter end and a receiver end.

Also, according to aspects, there is provided a method and apparatus for generating a codebook in a multi-polarized MIMO system that can reconstruct a precoding matrix according to a transmission rank and thereby can more effectively generate a codebook.

Also, according to aspects, there is provided a method and apparatus for generating a codebook in a multi-polarized MIMO system that can generate a rotated matrix when the polarization direction of transmitting antennas is rotated, and thereby can more flexibly cope with a change in the polarization direction.

As described from the foregoing, a codebook with low complexity and excellent performance and robustness can advantageously be obtained for use in multi-polarized MIMO schemes. Such codebook design can also be used for single-polarized MIMO schemes without any significant performance degradation.

Various components of the codebook generation apparatus, as shown in FIG. 5, such as, the single-polarized precoding matrix assignment unit 510, the zero matrix assignment unit 520, the precoding matrix generating unit 530, the precoding matrix reconstruction unit 540, the rotate precoding matrix generation unit 550 and the phase adjustment unit 560 can be integrated into a single control unit, such as a baseband processor or controller located at a transmitter side, for example, a base station, or alternatively, can be implemented in software or hardware, such as, for example, a field programmable gate array (FPGA) and an application specific integrated circuit (ASIC). As such, it is intended that the processes described herein be broadly interpreted as being equivalently performed by software, hardware, or a combination thereof. As previously discussed, software modules can be written, via a variety of software languages, including C, C++, Java, Visual Basic, and many others. These software modules may include data and instructions which can also be stored on one or more machine-readable storage media, such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; and optical media such as compact discs (CDs) or digital video discs (DVDs). Instructions of the software routines or modules may also be loaded or transported into the wireless cards or any computing devices on the wireless network in one of many different ways. For example, code segments including instructions stored on floppy discs, CD or DVD media, a hard disk, or transported through a network interface card, modem, or other interface device may be loaded into the system and executed as corresponding software routines or modules. In the loading or transport process, data signals that are embodied as carrier waves (transmitted over telephone lines, network lines, wireless links, cables, and the like) may communicate the code segments, including instructions, to the network node or element. Such carrier waves may be in the form of electrical, optical, acoustical, electromagnetic, or other types of signals.

In addition, similar to above, the codebook generating method as shown in FIG. 2 may be recorded, stored, or fixed in one or more computer-readable storage media that includes program instructions to be implemented by a computer to cause a processor to execute or perform the program instructions. The media may also include, alone or in combination with the program instructions, data files, data structures, and the like. The media and program instructions may be those specially designed and constructed, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable media include magnetic media, such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM disks and DVDs; magneto-optical media, such as optical disks; and hardware devices that are specially configured to store and perform program instructions, such as read-only memory (ROM), random access memory (RAM), flash memory, and the like. Examples of program instructions include machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. The described hardware devices may be configured to act as one or more software modules in order to perform the operations and methods described above, or vice versa. In addition, a computer-readable storage medium may be distributed among computer systems connected through a network and computer-readable codes or program instructions may be stored and executed in a decentralized manner.

As a non-exhaustive illustration only, the devices described herein may refer to mobile devices such as a cellular phone, a personal digital assistant (PDA), a digital camera, a portable game console, and an MP3 player, a portable/personal multimedia player (PMP), a handheld e-book, a portable tablet and/or laptop PC, a global positioning system (GPS) navigation, and devices such as a desktop PC, a high definition television (HDTV), an optical disc player, a setup and/or set top box, and the like, consistent with that disclosed herein.

A computing system or a computer may include a microprocessor that is electrically connected with a bus, a user interface, and a memory controller. It may further include a flash memory device. The flash memory device may store N-bit data via the memory controller. The N-bit data is processed or will be processed by the microprocessor and N may be 1 or an integer greater than 1. Where the computing system or computer is a mobile apparatus, a battery may be additionally provided to supply operation voltage of the computing system or computer.

It will be apparent to those of ordinary skill in the art that the computing system or computer may further include an application chipset, a camera image processor (CIS), a mobile Dynamic Random Access Memory (DRAM), and the like. The memory controller and the flash memory device may constitute a solid state drive/disk (SSD) that uses a non-volatile memory to store data.

A number of examples have been described above. Nevertheless, it will be understood that various modifications may be made. For example, suitable results may be achieved if the described techniques are performed in a different order and/or if components in a described system, architecture, device, or circuit are combined in a different manner and/or replaced or supplemented by other components or their equivalents. As an example, the antenna arrangement, shown in FIGS. 1A-1C, typically includes a transmitter side provided with transmitting antennas X₁ . . . X_(M) and a receiver side provided with N receiver antennas Y₁ . . . Y_(N) to communicate, via a wireless channel (channel matrix H). For mobile communication systems, a base station (BS), known as “Node-B” as specified in accordance with 3GPP, 3GPP2 and 4G specifications, is used at the transmitter end to transmit data, via wireless channels. User equipments (UEs), typically mobile stations (MS), are used at the receiver end to receive data, via the wireless channels. Such user equipments (UE) can be, for example, mobile phones (handsets), personal digital assistants (PDAs), or other devices such as wireless cards in laptop computers or computers with internet wireless connectivity, WiFi and WiMAX gadgets etc. The wireless network can be that of any of the wireless communication technologies, including, but not limited to GSM (Global System for Mobile Communications), CDMA (Code Division Multiple Access), WLL (Wireless Local Loop), WAN (Wide Area Network), WiFi, and WiMAX (Worldwide Interoperability for Microwave Access based on IEEE 802.16 standards), and is applicable with many existing and emerging wireless standards such as IEEE 802.11 (for wireless local area networks), IEEE 802.16 (for wireless metropolitan area networks) and IEEE 802.02 (for mobile broadband wireless access). The base station (BS) can also be an IEEE 802.11 access point (AP) and the UE can also be any client station. Alternatively, the base station can also be implemented with a GERAN (GSM/EDGE radio access technology) in a UTRAN (UMTS Terrestrial Radio Access Network) using a wideband code division multiple access (WCDMA) technology. However, embodiments are not limited to those radio access technologies, but it can also be applied to the following radio access technologies: GSM (Global System for Mobile Communications), GPRS (General Packet Radio Service), E-GPRS (EDGE GPRS), CDMA2000 (CDMA, Code Division Multiple Access), US-TDMA (US Time Division Multiple Access), and IS-95. Accordingly, other implementations are within the scope of the following claims. 

1. A communication apparatus for a communication between a transmitter having eight transmit antennas and a receiver having at least one receive antenna, the communication apparatus comprising: a codebook storage unit configured to store at least one matrix W_(i) comprising eight rows, where i is a natural number; and a precoder configured to precode a data stream desired to be transmitted based on one of the stored at least one matrix W_(i), wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), comprises a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, comprises the zero matrix.
 2. The communication apparatus of claim 1, further comprising: an information receiver configured to receive information associated with a matrix selected by the receiver from the stored at least one matrix W_(i), wherein the precoder is further configured to precode the data stream based on a precoding matrix generated based on information associated with the selected matrix.
 3. The communication apparatus of claim 1, wherein each of the at least one matrix W_(i) comprises: a transmission rank of 2; and a dimension of 8×2.
 4. A communication apparatus, comprising: a codebook configured to be used for a communication between a transmitter comprising eight transmit antennas and a receiver comprising at least one receive antenna, the codebook comprising at least one matrix W, comprising eight rows, i being a natural number, each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), comprising a nonzero matrix, the nonzero matrix excluding a zero matrix, each remaining block, excluding the diagonal blocks, comprising the zero matrix.
 5. The communication apparatus of claim 4, wherein each of the at least one matrix W_(i) comprises: a transmission rank of 2; and a dimension of 8×2.
 6. A communication apparatus for a communication between a transmitter comprising eight transmit antennas and a receiver comprising at least one receive antenna, the communication apparatus comprising: a codebook storage unit configured to store at least one matrix W_(i), where i is a natural number; a selector configured to select, as a target matrix, one of the stored at least one matrix W_(i); and an information feedback unit configured to feed back information associated with the target matrix to the transmitter, wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), comprises a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, comprises the zero matrix.
 7. The communication apparatus of claim 6, wherein the selector is further configured to select the target matrix in response to a pilot signal transmitted from the transmitter.
 8. The communication apparatus of claim 6, wherein the information feedback unit is further configured to feed back index information of the target matrix.
 9. A communication method for a communication between a transmitter comprising eight transmit antennas and a receiver comprising at least one receiver, the communication method comprising: generating a precoding matrix based on one of at least one pre-stored matrix W_(i) comprising eight rows, where i is a natural number; and precoding a data stream desired to be transmitted based on the one of at least one matrix W_(i), wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), comprises a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, comprises the zero matrix.
 10. The communication method of claim 9, further comprising: receiving, by a receiver, information associated with a matrix selected by the receiver from the stored at least one matrix W_(i); and precoding the data stream based on a precoding matrix generated based on information associated with the selected matrix.
 11. The communication apparatus of claim 9, wherein each of the at least one matrix W_(i) comprises: a transmission rank of 2; and a dimension of 8×2.
 12. A non-transitory computer-readable medium comprising a program to instruct a computer to implement the method of claim
 9. 13. A communication method for a communication between a transmitter comprising eight transmit antennas and a receiver comprising at least one receive antenna, the communication method comprising: selecting, as a target matrix, one of pre-stored at least one matrix W_(i), where i is a natural number; and feeding back information associated with the target matrix to the transmitter, wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), comprises a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, comprises the zero matrix.
 14. The communication method of claim 13, wherein each of the at least one matrix W_(i) comprises: a transmission rank of 2; and a dimension of 8×2.
 15. A non-transitory computer-readable medium comprising a program to instruct a computer to implement the method of claim
 13. 16. A communication method for a communication between a transmitter comprising eight transmit antennas and a receiver comprising at least one receive antenna, the communication method comprising: storing at least one matrix W_(i), where i is a natural number; selecting, as a target matrix, one of the stored at least one matrix W_(i); and feeding back information associated with the target matrix to the transmitter, wherein each diagonal block, among a plurality of blocks included in each of the at least one matrix W_(i), comprises a nonzero matrix, the nonzero matrix excluding a zero matrix, and wherein each remaining block among the plurality of blocks, excluding the diagonal blocks, comprises the zero matrix.
 17. The communication method of claim 16, further comprising selecting the target matrix in response to a pilot signal transmitted from the transmitter.
 18. The communication method of claim 16, further comprising feeding back index information of the target matrix.
 19. A non-transitory computer-readable medium comprising a program to instruct a computer to implement the method of claim
 16. 20. The communication apparatus of claim 1, wherein the feedback starts initially and restarts periodically, by sending a one-shot feedback that fully depicts the precoder by itself.
 21. The communication apparatus of claim 6, wherein the feedback starts initially and restarts periodically, by sending a one-shot feedback that fully depicts the precoder by itself.
 22. The communication method of claim 9, further comprising starting the feedback initially and restarting the feedback periodically, by sending a one-shot feedback that fully depicts a precoder by itself.
 23. The communication method of claim 13, further comprising starting the feedback initially and restarting the feedback periodically, by sending a one-shot feedback that fully depicts a precoder by itself.
 24. The communication method of claim 16, further comprising starting the feedback initially and restarting the feedback periodically, by sending a one-shot feedback that fully depicts a precoder by itself.
 25. The communication apparatus of claim 6, wherein a total number of bits of fed back is
 120. 26. The communication method of claim 13, wherein a total number of bits of fed back is
 120. 